Maybe it is because I don't like shopping, but to me this is one of the most boring things you can do in Ubud. It is right in the center of town so it is sort of unavoidable, but unless you enjoy haggling over a t-shirt or seeing 1000 variations of 'original' Balinese key rings you can just ignore it.
If you like produce and vegetables and local life come at dawn and buy all sorts of tropical fruits and some cheap snacks to keep you going for the rest of the day.

The art market has a lot of artifacts and sculptures. Though the initial prices are high, one can use their bargaining skills to bring the prices down.

This is a great place to shop for everything Bali related and in my experience its was cheaper than in kuta. Also compared to krisna , stuff is still cheaper.

The key to good shopping here is being able to haggle. The people selling maybe give you a high price but it is almost expected that you ask for a better price.

Ladies, the rattans!!! My haggling strategy was just to set a fair price and stick to it. I cant do the back and forth thing. I managed to get the rattans (real straw one) for 120k, the silk dresses for 150 I, the batik robe for 150k and the silver rings , 2 for 50 k.

You can get sarongs here at 25 k each. Take advantage of this. I paid 50 for the same thing in kuta, that was after the haggling.

I held back on my shopping in Ubud after hearing so much about krisna souvenir store. Totally regret that decision. Except the t shirts and key chains, ubud art market is still cheaper, especially with jewelry and rattans and it also offers more variety.

You may get a little put off because it looks a bit dodgy but it is perfectly safe.

For leather goods, I recommend the markets at Goa Gajah though.